Journal of Urban Management 4 (2015) 24–39
Research Article
Time dependent accessibility
Nikhil Kaza
Department of City and Regional Planning, University of North Carolina at Chapel Hill, Campus Box 3140, Chapel Hill, NC 27599-3140, United States
Received 26 February 2015; received in revised form 1 June 2015; accepted 2 June 2015 Available online 3 July 2015
Abstract
Many place based accessibility studies ignore the time component. Relying on theoretical frameworks that treat distance between twofixed points as constant, these methods ignore the diurnal and seasonal changes in accessibility. Network distances between two nodes are dependent on the network structure and weight distribution on the edges. These weights can change quite frequently and the network structure itself is subject to modification because of availability and unavailability of links and nodes. All these reasons point to considering the implications of volatility of accessibility of a place. Furthermore, opportunities have their own diurnal rhythms that may or may not coincide with the rhythms of the transportation networks, impacting accessibility. Using the case of transit, where all these features are readily apparent simultaneously, I demonstrate the volatility in accessibility for two counties in North Carolina. Significant diurnal changes are observed in quarter of the locations and in the rest the changes are minimal mostly because of low levels of transit accessibility. I argue not for minimizing the volatility, but for acknowledging its impacts on mode choices, location choices and therefore on spatial structure of cities.
& 2015 The Author. Production and Hosting by Elsevier B.V. on behalf of Zhejiang University and Chinese Association of Urban Management. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Accessibility; Public transportation; Social justice
1. Introduction
Many studies on transportation accessibility assume that the underlying spatial topology is invariant. Borne out of a Newtonian conceptualization of space, accessibility is measured as either as a cumulative measure of opportunities that are available from a location at a certain distance (or other appropriate metric such as travel time) or weighted measure usually based on gravity or a random utility (for discussion see El-Geneidy & Levinson, 2006;Handy & Niemeier, 1997). In each of these approaches, there are no diurnal or seasonal changes in the distance metric between any two given points in space. The underlying assumption is that distance metric ( e.g. Euclidean/Manhattan) in a Cartesian plane is time invariant. The differences in the accessibility of a location then usually stems from the changes of the attributes of the locations and attractors (e.g. employment, destination types, types of households etc.) and the interest is usually on relative accessibility of one location with respect to another (Dalvi & Martin, 1976). In this paper, I want to argue that accessibility also depends upon the variable distance metric and should be given adequate attention.
www.elsevier.com/locate/jum
http://dx.doi.org/10.1016/j.jum.2015.06.001
2226-5856/& 2015 The Author. Production and Hosting by Elsevier B.V. on behalf of Zhejiang University and Chinese Association of Urban Management. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
E-mail address:[email protected]
A Leibnitzian conception of space, by contrast, is a conceptualization of space that dependent on locations of objects relative to one another (Galton, 2001). Despite this abstractness, I argue that such mode of thinking allows us to rethink the distance metric as a variable and lends itself particularly well to a imagining a topological structure that changes over time. However, the network distance between two nodes is invariant, only if the underlying network structure is invariant. Many accessibility analyses not only focus on relative accessibility of locations, but also on relative changes in accessibility once a set of infrastructure investments (changes to network structure) are made (e.g.
Golub, Robinson, & Nee, 2013). Furthermore, when travel times are used as measure of impedance, the distance
metric during peak and off-peak hours between any two given points are different even without any physical changes to the network; the edges shorten and lengthen depending on the time of the day. In other words, the weighted network changes with time (though the weights remain finite).
Consider the scenario where particular nodes or edges are no longer available. This situation is quite common during hazardous events (Litman, 2006) when some links and nodes disappear from the networks (or the weights become infinite) and therefore depending on their centrality can dramatically change the network distances between any two given nodes. This is another case of variant topological network. Thus, space with variable topological structure is not uncommon. All the above examples presented make a compelling case for considering the variable distance metric. There is perhaps a no better use case than transit that encompasses all the above situations. Even within an hour, the impedance between any two nodes (stops) is varying because of intermittent schedules and wait times.
However, until recently even transit accessibility is still measured using invariant topological networks (Mavoa, Witten, & McCreanor, 2012;Tomer, Kneebone, & Puentes, 2011). These invariant networks usually assume a transit network during the peak morning commute. Automobile remains a dominant mode compared to transit, because it not only widens the spatial aspects of accessibility but the temporal aspects as well (Clifton, 2004). This is particularly true for non-work activities that fall outside the traditional work day schedule. Infrastructure support for bread-winning is the norm because of gendered assumptions that undergird planning analyses (Clifton, 2004;Law, 1999), and the transit provision is biased towards peak hours and work days.
Unlike automobiles because the underlying network structure is dependent on un/harmonized schedules between different lines in the transit system that facilitate transfers, changes in these levels of service on a single line has ripple effects through the entire system. Depending on the time of the day, a line in the transit system may not be running and thus removing a set of links and nodes from the network. Thus, the impedance metric is very elastic within a single day and between weekdays and weekends. All these features make the case for using understanding the temporal patterns of transit accessibility, as there are analogues in other situations described earlier.
It is, therefore, useful to study how the periodicity and breaks in the patterns of transit accessibility. It provides a starting point for understanding changes in other accessibility metric (such as automobile) instead of relying on the maxmin approach that underlies the consideration of peak travel times, or worse using max approach that ignores congestion all together.
Furthermore, accessibility that only accounts for invariant impedance is usually based upon the assumptions that travel to work, and more insidiously, travel to particular kind of work (regular shift) is singularly important. Using Current Population Survey data from 2004,McMenamin (2007)claims that almost 30% of the US workers are able or constrained to work in shifts other than regular shifts. Furthermore, accessibility to amenities other than work is also important (Handy & Clifton, 2001) and because these amenities such as restaurants, retail establishments, hospitals have different rhythms than a traditional 9-5 job, changes in accessibility during the day and by seasons have implications both for users of as well as those employed at these amenities (Weber & Kwan, 2002).
In their wide ranging review,Geurs and van Wee (2004)suggests that accessibility should account for land-use component, transportation component, temporal component and personal component. They suggest that each of these components is indirectly related to one another.Mamun et al. (2013)use a different approach to account for temporal coverage by accounting for per capita service frequency and distance decay factor. In this paper, I want to argue that there are more direct relationships and should be accounted for our in our measures of accessibility. While the spatial distribution of opportunities is important, it is also related to the temporal dimensions of these distributed opportunities (activity hours, duration etc.) (Crang, 2004). The temporal component not only affects the time available for opportunities by a person, but also whether or not such opportunities can be accessed by a person by a particular mode and with a reasonable cost.
Furthermore, standard equity analysis for transit either measures the level of service in traditionally underserved areas by either measuring the headways or the number of jobs accessible via transit without actually accounting for whether such accessibility is constrained by time of the day. Such constraints are important to consider for equity analysis because, more often than not, persons in low income areas and underserved groups are likely to have non-traditional work arrangements and have significantly larger number of household maintenance trips that occur via transit and which may or may not be during regular ‘peak’ hours and therefore are more likely to suffer from low levels of transit service and large investments in auto-oriented development (Bullard, Johnson, & Torres, 2004).
To support these arguments, I begin by conceptualizing different accessibility measures and putting the place based accessibility measures into a single framework. I modify this framework to demonstrate that time could be readily incorporated and show for the case of transit how the method can be readily applied for much of the United States. I demonstrate the results of a specific case for two county region in North Carolina and draw some implications. Finally, the limitations of this study are acknowledged providing directions for future research.
2. Conceptual overview and methods
In their scathing critique, Kwan and Weber (2003) argue for the decline of the importance of distance1in our conceptual understanding and explanation of the urban spatial structure and transportation behavior and location choice. Giving examples of number of studies that showed mixed results about the relationship of distance to the central business district with level of employment, and housing values they argue that new models of accessibility are required that would account for the temporal constraints on different individuals as well the problems associated with place based accessibility measures. They advocate for a person based accessibility measures that follow from
Hägerstrand's (1970) conception of opportunities based on personal scheduling constraints (Miller, 1999) and for
explicitly accounting for the temporal changes in space (e.g. Neutens, Delafontaine, & Scott, 2012).
However, accessibility analysis is replete with place-based models instead of person-based models. Some of the main reasons are (1) place is an important aggregative mechanism that summarizes the experiences of persons, (2) planners and decision makers have abilities to affect places through infrastructure improvements, in more direct ways than they could affect persons and (3) data to compute personal accessibility because of individual scheduling constraints are hard to come by. Therefore it is of no surprise that place based models are still a common theme in the literature. The method proposed here bridges place based accessibility and space-time based measures and require only readily available data.
In general, accessibility of a place i, with K as a set of destinations is defined as Ai¼
X
jA K
gðOjÞf ðdijÞ
In a distance-based measure of accessibility, j refers to specific destinations such as central business district or bus stops, gðOjÞ ¼ 1 and f ðdijÞ ¼ dij where dij is the distance between j and i. In cumulative opportunities and gravity
based models, gðOjÞ is the number of opportunities (usually jobs) at location j or some other metric such as economic
activity. Cumulative opportunities and gravity based measure are the same except for the weighting function. In the former case, the weighting function f, is an indicator functionχdijo D, where D is the threshold distance and in the
latter case, it usually is eβdij, whereβ is the decay parameter.
For the purposes of this analysis, the functional forms of f and g are largely irrelevant as the analysis is focused on the variability with respect to time. Therefore, I choose to demonstrate the concepts using the cumulative opportunities measure, though apart from computational considerations, there are no barriers in applying them to other place based accessibility measures. Accessibility of a place that is conditioned on time t is recast as
Ati¼X jA K χtA TðO T jÞχdt ijo Dðd t ijÞ where OT
j is the number of opportunities (jobs) at a location j with duration T andχð:Þ is a indicator function. I use
two modes (walking and bus) to compute dtij, which could also be extended to use other compatible modes that
1Because geographic distance and travel time are both distances in different metric spaces, I use distance to refer to them both in the rest of
would allow mode shifts such as bicycle. Since I am interested in place based accessibility and equity implications, I choose block group centroids as the origins and individual establishments as the set K. With appropriate modifications, the same analysis can be conducted for a purely zonal or purely point geographies conditioned on the availability of the data.
This kind of formulation is not novel.Polzin, Pendyala, and Navari (2002)uses time-of-day based accessibility using a hypothetical two route transit network. However, their work is focused on capturing demand by incorporating headways and spans. Perhaps the most similar formulation is byAnderson, Owen, and Levinson (2013)and Owen
(2013). They use the transit schedules in Twin Cities, Minnesota to capture time dependent transit access in 1 min
throughout the day. While they account for the variation in the transit schedule they do not account for the temporal variation in the available opportunities. In a similar study to this one,Farber, Morang, and Widener (2014)studied the temporal accessibility of supermarkets and the disparities among different racial groups, by considering the differences in transit provision and schedules, but do not consider duration of opportunity. The current study focuses all time dependent employment and not just supermarkets.
The algorithm follows roughly the same logic asLei, Chen, and Goulias (2012)and heavily uses the python code fromMorang and Pan (2013)(seeFig. 1). The transit network is built from the Transit agencies’ Generalized Transit File Specification (GTFS) files that are freely available online. Because in general, there are many transit agencies in a region that have operations that are complementary, I use multiple relevant GTFS files for a region to create a database for stops, links and schedules. The transit network is merged with road network from OpenStreetMap (OSM) that includes both limited access highways and local roads. To reach a transit station and other destinations from transit stations, I use a walking speed of a constant 4.8 km/h on the road network (seeKrizek, El-Geneidy, & Iacono, 2007). Then feasible origin destination pairs are calculated based on the schedule of the transit lines using Dijkstra’s algorithm that is built in the ArcGIS™ Network Analyst. Block group centroids or Origins are attached
GTFS Files OSM
Streets
Compute O-D travel time between stops
Modified Block Group Centroids Travel to Nearest Stop (Walk) Travel to Destination Stops (Transit)
Walk to nodes on road network for remaining time
Compute service area polygons Start Time Update start time Compute cumulative opportunity for each
start time Fig. 1. Schematic of the algorithm.
to the nearest node on the merged network and service area buffers are computed for each origin for every 10 min in the day. These service area buffers consider the feasible destinations based on both walking and transit and automatically includes wait times and transfers to different lines. Because GTFS identifies schedules by different days, I compute these buffers both for a typical weekday, Saturday and Sunday. This could also be extended to include seasonal variations as long as the GTFS data has the information. To reduce the computational time, I limit the analysis only to block groups that are close (within 3.6 km) to transit stations.2Employment within the buffers is calculated for each buffer and is assigned to block groups as a measure of accessibility for that particular time. Thus, creation of these buffers can be replicated anywhere in the United States where OSM and GTFS files are readily available.
While I do not use this dataset in this analysis, synthetic employment from Longitudinal Employer-Household Dynamics dataset can be used for destinations with information about their industry classification. Duration, T, as defined by facility opening hours are not comprehensive in standard data sources like Google or Yelp for all establishments in all industry types.3Therefore, broad activity hours are inferred for each of the industry classes: 8 am–6 pm for most industries, 6 am–2 am for food service (NAICS 722),410 am–11 pm for retail (NAICS 44-45) are used to categorize the establishments and employment. These times are inferred from queries using sample of names of the establishment to the Google places API.5This is not ideal unlike Ahas et al. (2010)study, which uses cellphone data to both spatially and temporally fix the activity patterns in the city.
3. An use case
The usefulness of the above concepts is demonstrated for a two county region; Orange and Durham Counties in North Carolina. These are the two main counties in the Durham-Chapel Hill-Carrboro Metropolitan Planning Organization (DCHC-MPO), which is responsible for transportation planning for the western part of the Research Triangle area in North Carolina.6Orange County is home to the University of North Carolina at Chapel Hill and Duke University is located in Durham County, both of whom are major employers in the region. The Research Triangle Park (RTP) is located Southern edge of Durham County, which is the home to many large employers and is not only the economic engine of the region but also for the state. Collectively, 0.4 million people call these counties their home and 333,822 are employed in these two counties in 34,241 establishments (seeTable 1). In total there are 228 block groups in the two counties region, and 18 of them are too far from transit stops so I ignore them from the analysis. In general, the transit provision seems to align with the density (see Fig. 2); i.e. most of the jobs and households are relatively close to transit. However, as we will see later, that this does not translate to accessibility. Like many regions, transit service in the triangle is splintered among multiple agencies (see Fig. 2). The main agencies that provide transit are Durham Area Transit Authority (DATA), Chapel Hill Transit (CHT) and Triangle Transit (TTA). Because these transit systems connect up with other transit agencies in the region, I also consider Capital Area Transit (CAT) and C-Tran system to build a master regional transit service stops and lines, even though they are not considered in the set of origins. All these organizations runfixed line bus services.7In total, there were 3967 bus stops and 135 routes during the regular weekday.
While there is regional effort underway to jointly plan for infrastructure improvements and provide a convenient trip planning interface, because of different mandates and organizational structures the operations are not necessarily coordinated. Chapel Hill Transit is a fare free system that relies on the contribution from the University where as the rest have fare structures that are not harmonized. Transfer from one system to the other is possible only with a regional bus pass, which is only sold online or at select stations. In this analysis, I also ignore these limitations and
2
With a walking speed of 4.8 km/h, this threshold eliminates destinations that can only be reached by walking in 45 min. The temporal variability of accessibility in such situations is conditioned only by the duration of the opportunity.
3Industries such as NAICS codes 722 (Food Services) and 44-45 (Retail) are oversampled in Google and Yelp databases that are available
through their Application Programming Interfaces (API).
4The North American Industry Classification System (NAICS) is the standard used by Federal statistical agencies in classifying business
establishments and is developed by Office of Management and Budget (OMB).http://www.census.gov/eos/www/naics/.
5https://developers.google.com/places/documentation/(accessed November 23, 2013).
6The MPO’s jurisdiction is not exactly same as the study area. The jurisdiction covers all of Durham and the urbanized portion of Orange
County and small portion of Chatham County. Since Chatham County does not havefixed route transit, it is not considered in the analysis.
consider only travel time as cost of travel instead of a generalized cost. I also limit the number of transfers to one and set the maximum travel time (D) to 45 min. The average commute time in the two county region is 23 min, so this upper limit is not unreasonable. Any arbitrary D can be chosen without loss of generality.
The GTFSfiles are available from http://www.gtfs-data-exchange.com/. The GTFS format is widely documented as they are used to create number of transit applications. In general, each agency provides a set offiles that include
Fig. 2. Regional context and transit systems in the study area. Wake county is shown for completeness, though is not used in the study area. The mixing of population and households are represented using a dot density plot; Bus lines from different transit agencies are also shown. (Source American Community Survey 2006–2010. GoTriangle.).
Table 1
Sectoral classification of employment and establishments in 2011 in the study region.
NAICS code Sector Count of establishments Employment
11 Agriculture, Forestry, Fishing and Hunting 394 975
21 Mining, Quarrying, and Oil and Gas Extraction 10 305
22 Utilities 19 511
23 Construction 2554 11,447
31–33 Manufacturing 914 30,477
42 Wholesale Trade 1010 6728
44–45 Retail Trade 2794 23,321
48 Transportation & Warehousing 560 4803
51 Information 829 6072
52 Finance and Insurance 1220 7576
53 Real Estate and Rental and Leasing 1902 8002
54 Professional, Scientific, and Technical Services 5431 36,680
55 Management of Companies and Enterprises 157 374
56 Administrative and Support and Waste Management and Remediation Services 7147 19,866
61 Educational Services 691 34,114
62 Health Care and Social Assistance 3142 94,903
71 Arts, Entertainment, and Recreation 684 3845
721 Accommodation 186 4831
722 Food Services and Drinking Places 668 10,914
81 Other Services (except Public Administration) 3749 13,905
“stops”, “routes”, “trips”, “stop_times” and “calendar” that combined together provide information on the schedule of every route during the day and the week.
I use the National Establishment Time Series (NETS) dataset to locate the employment and establishments. This proprietary dataset is from Walls & Associates, who convert Dun and Bradstreet (D&B) archival establishment data into a time series. For our analysis we ignore the longitudinal information in the dataset and focus on the establishments present in 2011 along with the number of employees and their industry category (NAICS 2007 definitions). Establishments near all transit stops (including outside the two counties) are extracted and are used in the analysis. As mentioned previously, LEHD data could be substituted for this dataset.
4. Results
I will discuss the results for all jobs without considering the characteristic function g(.)first and then discuss the time dependent accessibility that constrains some sectors more than others. As can be expected in the use case, large percentage of block groups (162 or 77%) does not exhibit any variation even in a weekday where schedules vary dramatically and transit is oriented towards work travel. While, it might be tempting to think then that the above analysis is futile, it should be noted that the block group with the maximum value accessibility has a value 1,231 compared to a maximum value of 129,573. It should also be noted that the maximum value of the just over half the total number of jobs in the two counties; i.e. almost half of the jobs have no transit access at anytime of the day from any location. Other invariant block groups have substantially less accessibility with only 22 block groups (10%) greater than 100. This is reflective of low levels of transit accessibility for a large portion of the region, rather than conceptual issues with the analysis. In other words, even if the block groups were relatively close to the bus stops, the schedules were arranged in such a way that within 45 min of combined walk and bus travel, many jobs are accessible to large areas in the region. The block groups with relatively high accessibility are essentially downtown areas in Durham, Chapel Hill and Carrboro areas, though not all of central city locations have the same high accessibility.
Fig. 4. Hourly median accessibility in each block group of Durham and Orange Counties. The lines are colored based on the proportion of the minorties and the break points reflect the median proportion in Orange County (0.27) and Durham County (0.56).
If we consider the characteristic function g(.) that is described earlier, the block groups with higher accessibility are adjacent to the major transportation corridors (seeFig. 3). The presence of a bus route does not translate to higher accessibility. The rest of the region has very poor transit accessibility reflecting the transportation investment priorities in the region. What is more interesting is the variation in diurnal and weekly accessibility. In the 49 block groups that do have relatively high levels of transit access (41,500 weekday median), the accessibility shows a strong cyclical pattern, with significant changes in the structure throughout the day ( ). These cyclical patterns are not uniformly experienced. To visualize the changes in the trends, it may be much more useful to smooth out the hourly cycles with medians. The median while being unaffected by extreme values is relatively sensitive to changes in both amplitude and frequency of the cycles and therefore it is relatively easy to detect the trend. A noticeable and consistent pattern of change can be observed in the sharp drop-offs in the accessibility between 6 PM and 7 PM on weekday, reflecting significant changes in the level of service post evening peak (seeFig. 4). In many cases, there is not a significant reduction in accessibility throughout the day post morning peak, though at least in a few block groups peaks are observed in the mid afternoon and around 10 am.
While block groups with highest accessibility in Durham County are above the median of the county’s proportion of minority population, in Orange County the situation is reversed (seeFig. 4). A strong discontinuity can be seen in accessibility in many block groups between 7 am and 9 am and a marked decline after 6 pm. The weekend and weekday accessibility is also markedly different reflecting the bias of the transit provision towards regular work shift. In some block groups, the accessibility declines during the middle of the day, suggesting smaller headways and higher frequency as well as more harmonized schedules during peak hours and less harmonized schedules in the off-peak period. The decline in the transit accessibility post 6 pm is as much as function of low levels as transit service as well as unavailability of opportunities.
It should also be noted that the same block groups have markedly lower accessibility during the weekend and with different patterns. Almost all the block groups that have relatively higher accessibility for most of part of the Saturday and Sunday are blocks in central Durham County. This is partly explained by two phenomena. DATA, unlike CHT does not have dramatically marked reduction in service on Saturday. Triangle Transit, the regional transit agency does not run its express lines on Saturday, runs its other lines with lower levels of service and does not provide any service on Sunday, which puts residents in Orange county at a disadvantage in accessing the jobs in Durham County.
One of the advantages of considering a time varying measure is to determine, which areas have abrupt and dramatic shifts in accessibility and if that is consistent with the regional transit planning goals. Shifts in a univariate time series can be found using methods described in Verbesselt et al. (2010). While the details of the method is beyond the scope of this particular paper, suffice it to say that the method uses iterative decomposition of the time series and detecting significant breaks using standard change detection methods (Zeileis, Kleiber, & Krämer, 2003). The advantage with the approach is the use of a harmonic seasonal model, which appropriate in our case given the nature of the data.
An example of break detection in the daily trend is shown in Fig. 5(a) for a block group in Orange County. Significant reduction in accessibility happens around 11 am through decrease in frequency of service and stays that way till 2 pm. After 6 pm, the accessibility is fairly low. The changes in the accessibility levels by visualizing the histogram of these breakpoints (Fig. 5(b)). Block groups in Durham County (left) have greater number of changes in the accessibility levels and these break points are distributed throughout the day. The breaks corresponding to the regular shift (around 10 am and 6 pm) can be discerned from the histograms.
Another way to visualize the differences over time is to use a multivariate time series plot (Peng, 2012). It is easy to pick out the sharp drop off in the values for Orange county (in purple) in the post evening peak time period, compared to Durham (seeFig. 6). However, when there is no such drop off, the right margin table indicates that the median over the day is relatively low suggesting low levels of accessibility over all. Thus the figure shows the tradeoffs between accessibility and quality. Reordering the rows of the plot by the decreasing order of the median value shows that for areas with very high accessibility (large daily median), the periodicity changes of the high values in the post evening peak compared to the rest of the day but nevertheless there are certain times of the night the accessibility is in the upper quintiles. This also explains the sharp drop in the hourly median of lines toward the top of the graph inFig. 4. In areas of very low accessibility (small daily median) the periodicity throughout the day is relatively constant.
Till now, we have discussed the temporal trends focusing only on the variability of the distance metric. However, as discussed above different organizations and therefore different places in the region have different rhythms and impact the accessibility. Shopping is usually an after hours activity and therefore unavailability of transit to serve these uses across the region (seeFig. 7(b)) contributes to the auto-orientation. Similarly, in the food service industry there are some establishments that cater to their customers during the day and others in the evening. Given the orientation of the transit system in the region, accessibility food establishments is relatively high throughout the day but declines quite rapidly post 6 pm (see Fig. 7(c)) across the board except for few places in Durham. The accessibility as indicated by regular shift employment show low levels during the midday and high levels during morning and evening peak (see Fig. 7(d)). Given that the orientation of the infrastructure provision towards supporting employees rather than users, this mismatch is perhaps inevitable.
Fig. 5. (a) Example of break point detection in the accessibility trend within a block group and (b) histogram of break points during the day in Durham (left) and Orange (right) counties.
Fig. 6. Multivariate time series plot of accessibility for the 49 block groups. Orange County block groups are at the top and Durham County is at the bottom. Shades of green (high) and purple (low) are used to describe within each block group time series. The right panel is the box plot for each block group; the bottom panel is the median for all block groups over time.
5. Implications for urban management
To explain the location choices and mode choices of households, traditional explanations have tended to use the ideas about levels of accessibility. What this paper has demonstrated is that level of accessibility is only a partial picture. For a household deciding on mode choice, variability in the levels of accessibility is an important consideration. Especially if the accessibility conditions are undergird by assumptions about the work and activity that happens at certain times of the day. To appreciate why many people choose particular locations, and more importantly particular modes such as automobiles, planners and city managers have to pay close attention to this volatility of accessibility. The volatility of accessibility within a day is significantly lower for automobiles compared to transit and therefore risk averse households could choose to drive instead of taking the transit if their own schedules are relatively uncertain or incongruent with the assumptions that transit agencies make. This variability is ignored not just in professional practice but also in academic research.
Ignoring time variability in accessibility studies has several reasons. One reason is practical. While some regions may have high quality transit (small headways, wide coverage and high connectivity), such regions are few and far between in
Fig. 7. Multivariate time series plots of accessibility of different time constrained sectors for different block groups (smoothed with a spline of 6 degrees of freedom). Orange County block groups are at the top and Durham County is at the bottom. Shades of green (high) and purple (low) are used to describe within each block group time series. The right panels are the box plot for each block group; the bottom panels are the median for all block groups over time.
the United States. It is thus of no surprise that accessibility studies have auto orientation with a convenient assumption of invariant impedance between two points on network. In auto orientation, such assumptions are perhaps reasonable because network distances are fairly constant and impedance only depends on congested speeds. Congestion on one particular link does not dramatically affect the over all impedance of the paths unless the edge betweenness of the link is high. Given that in the US, only limited access highways have high edge betweenness, modeling accessibility by auto based on the congested speeds may give a reasonable picture of the relative desirability of places. In urban areas, congestion can dramatically affect accessibility. However, consideration of peak travel time reflects the maximin approach, which provides the best charactersation of the worst accessibility and this may be sufficient.
Another reason is conceptual. Because of high importance placed on work, infrastructure investments are focused on accessibility to jobs not on opportunities. According to the 2009 national household travel survey (NHTS) that 83% of the trips in the US are non-work trips. A recent Brooking’s study states that one of the common reasons for taking public transit is to go to work (Tomer et al., 2011), ignoring the fact that work related travel by public transit represented only 1/3 of the trips taken on public transit (Santos, McGuckin, &
Nakamoto, 2011). Even while the neat division of breadwinning at work and caregiving at home has been
upended since the World War II, yet transportation and transit investment decisions primarily are geared towards work-based travel. The rending of caregiving from home has important implications for travel behavior (on trip lengths, purposes and modes) and are yet to be systematically accounted for. Even though this paper, considers jobs as part of the accessibility calculations, it uses them as a proxy for opportunities by considering the duration of availability of opportunity.
Concomitant to the focus on work, another conceptual blind spot is the time of work. While a vast majority of the workforce does work in regular shifts, a great number do not. Shopping assistants, restaurant cooks and servers, building custodians, factory workers, domestic workers and a number of others work different shifts than a regular shift and those employees who are mostly likely to benefit from transit provision are usually ignored in the standard equity analysis by focusing on number of jobs available at a single time of the day.
While these reasons can partially explain why usually travel time variations are not considered in accessibility studies, until recently there has not been a widespread availability of networks with varying impedances and more importantly understanding of the temporal rhythms of a city. With the advent of ubiquitous personal tracking mechanisms via cellphone locations, we now see the city as a place not merely of economic activity, but of wide ranging sociocultural activities. This study aims to provide a framework using widely available datasets.
While, person based measures have long recognized the importance of time, constraints and budgets, place based measures have been reluctant to embrace them. Because person based measures require significant amount of data, this framework allows land use and transportation planners to consider how the temporal patterns of activities might be affecting the spatial patterns using widely available datasets.
I have demonstrated in the use case that places with relatively high accessibility during certain portions of the day do not have the same levels, during other portions. Someone who is likely to make choices about locations or choices about modes, would not only consider the levels but volatility as well. Lei et al (2012) posit that part of the explanation of low levels of transit usage in Southern California is because of comparatively low levels of transit accessibility to auto accessibility. However, another part of the explanation is the volatility of transit accessibility. It is operationally infeasible to eliminate the volatility in the transit service given the densities and preferences of travellers. In 2011, on average, 9 people are on a transit bus representing only 22% utilization rate in the United States (Center for Transportation Analysis, 2013, Table 2.12). Thus, across the board increases in the levels of service to match auto-oriented accessibility are unwise. Such increases should only be justified with concomitant changes to land use patterns and activity patterns. What I am arguing for is a careful accounting of how temporal volatility might be affecting location choices of users. Furthermore, as I have demonstrated in the use case, since there are many transit operators with different mandates and funding mechanisms, the operational considerations of each one of them might dramatically affect the accessibility patterns of users that are not necessarily in their ‘jurisdiction’. Thus, coordination is imperative.
One of the advantages of pegging accessibility to both place and time is that users can construct a composite accessibility based on multi-destination tours that can have an arbitrary start time. Choices of both housing locations as well as intermediate destinations may be conditioned by the level of accessibility at each location and at particular times. Future research could explore these connections.
6. Caveats
There are a number of caveats to this study that arise from practical data and computational considerations that warrant a brief mention. While I have argued that we should account for temporal variability, I have essentially sampled the times uniformly throughout the day. However, as it is apparent, the start time is of critical importance and can affect the nodes that can be reached within a certain time. Therefore, it might be useful to sample with as high a resolution as possible to get a more accurate picture, only to be limited by computational capabilities. However, much of this analysis can be naively parallelized by running the analysis for each hour on a different node in a cluster and then aggregating the results back.
Since this analysis should be considered demonstrative, I believe a 10 min interval is sufficient. To support this, I calculate the accessibility for one block group (in the middle of the accessibility spectrum of the region) and compare the results to the 10-min calculations (see Fig. 8). As expected, while there are some differences based on the resolution, the 10-min intervals provide a useful representation of the time dependency. The coefficient of variation for hourly interval using the 10-min and 1-min accessibility measure show high correlation (0.95). However, systematic study of the choice of the time resolution could be the focus of future research.
Hewko, Smoyer-Tomic, and Hodgson (2002)argue that all accessibility analysis suffer from spatial aggregation
errors and some spatial aggregation errors are more serious than others. They demonstrate for the case of Alberta that aggregation errors are a concern when calculating accessibility to amenities that have highly localized service areas such as playgrounds. In this analysis, I use a single point to represent block groups, which might have quite diverse distribution of population within them and therefore affect travel time to the nearest stop. Again this is an issue of resolution and computational limits force particular choices. The block groups in the two counties have a median population of 1,643 and a standard deviation of 811.1. In general, accessibility is higher in denser block groups (see
Fig. 3). The spatial resolution problem should be acknowledged, even when many studies use much coarser
geographies (such as census tracts).
Putting the spatial and temporal resolution concerns aside, the area of most concern is the resolution of the industry categorization and the use of industry types of infer the activity durations. Given the lack of data, this is the best that is possible. Capturing the temporal patterns in standardly available datasets would be a useful addition that would increase the value of these types of analyses. Furthermore, there is no reason to limit to using jobs as an indicator or ‘attraction’ of a location. Other data such as 'sales', 'ratings', are becoming widely available. If one of the critiques of this paper is to move away from conceptualizing accessibility of workers to accessibility of users then using jobs as a measure of quality of a place is perhaps not the most useful one. Furthermore, destinations such as playgrounds,
daycare centers, hospitals, libraries, movie theaters and restaurants might be more important than across the board establishments.
7. Conclusions
On a bus back from the airport in the mid-afternoon, I overhead a fellow passenger lamenting that his work trip on a bus takes over two hours, including transfers. During peak hours, when alternative routes were available, the trip to work would not have taken such a long time. This snippet of conversation prompted me to rethink if the standard measures of accessibility captured the lived experiences.
What I have demonstrated in this paper, is that real distances vary over time even within a day and therefore, it is not unreasonable to expect that perceived costs are also quite different for different modes. Because transit is schedule dependent, it captures various features that are usually ignored in accessibility studies: We can easily visualize, in the case of transit, the changes in network structure and the associated robustness of accessibility and these can be ported to other modes. We can also examine which routes are central to determining the accessibility of the region by examining the changes in the accessibility when the level of service on the route changes and therefore determine the importance of particular links. Because institutional structure of transit provision is usually fragmented, studies such as this highlight the importance of coordination of schedules and operations.
Ultimately, any measure of accessibility is imperfect reflection of the lived experience of the people. However, ignoring a key aspect, volatility, and focusing only on the level, can lead us misfocus infrastructure investments and programs. The key point of this study is to demonstrate that such volatility matters and ignoring it is underpinned by larger theoretical assumptions. Challenging such theoretical frameworks could help us in uncovering the role of accessibility in location choices and spatial structure of our places.
Acknowledgments
Louis Merlin and Noreen McDonald commented on early drafts of the paper. Figs. 2&3 were created by Josh McCarty. Anonymous reviewers and editors made helpful suggestions that improved the paper. Part of this work is funded by the Carolina Transportation Program. I am grateful for all their help, while retaining the responsibility for errors.
References
Ahas, R., Aasa, A. Silm, S. Daily rhythms of suburban commuters’ movements in the Tallinn metropolitan area: Case study with mobile positioning data. Transportation Research Part C: Emerging Technologies, 18(1), 45–54.
Anderson, P., Owen, A., & Levinson, D. M. (2013). The time between: Continuously defined accessibility functions for schedule-based transportation systems. Available from:〈http://trid.trb.org/view.aspx?id=1242878〉Accessed 12.5.14.
Bullard, R. D., Johnson, G. S., & Torres, A. O. (2004). Highway robbery: Transportation racism & new routes to equity. Cambridge, MA: South End Press.
Center for Transportation Analysis, A. O. (2013). Transportation energy data book Available from. (32nd ed.). Oak Ridge, TN: Oak Ridge National Laboratory.
Clifton, K. J. (2004). Mobility strategies and food shopping for low-income families a case study. Journal of Planning Education and Research, 23 (4), 402–413.
Crang, M. (2004). Rhythms of the city: Temporalised space and motion. In: J. May, & N. Thrift (Eds.), Timespace: Geographies of temporality (pp. 187–207). New York, NY: Routledge.
Dalvi, M. Q., & Martin, K. (1976). The measurement of accessibility: Some preliminary results. Transportation, 5(1), 17–42.
El-Geneidy, A. M. & Levinson, D. M. (2006). Access to destinations: Development of accessibility measures. Available from:〈http://trid.trb.org/
view.aspx?id=789631〉Accessed 19.11.13.
Farber, S., Morang, M. Z., & Widener, M. J. (2014). Temporal variability in transit-based accessibility to supermarkets. Applied Geography, 53(0), 149–159.
Galton, A. (2001). Space, time, and the representation of geographical reality. Topoi, 20(2), 173–187.
Geurs, K. T., & van Wee, B. (2004). Accessibility evaluation of land-use and transport strategies: Review and research directions. Journal of Transport Geography, 12(2), 127–140.
Golub, A., Robinson, G., & Nee, B. (2013). Making accessibility analyses accessible: A tool to facilitate the public review of the effects of regional transportation plans on accessibility. Journal of Transport and Land Use, 6(3), 17–28.
Handy, S. L., & Clifton, K. J. (2001). Evaluating neighborhood accessibility: Possibilities and practicalities. Journal of Transportation and Statistics, 4(2/3), 67–78.
Handy, S. L., & Niemeier, D. A. (1997). Measuring accessibility: An exploration of issues and alternatives. Environment and Planning A, 29(7), 1175–1194.
Hewko, J., Smoyer-Tomic, K. E., & Hodgson, M. J. (2002). Measuring neighbourhood spatial accessibility to urban amenities: Does aggregation error matter? Environment and Planning A, 34(7), 1185–1206.
Krizek, K., El-Geneidy, A. Iacono, M. Access to destinations: Refining methods for calculating non-auto travel times. Access to destinations study. Minneapolis, MN: University of Minnesota.
Kwan, M.-P., & Weber, J. (2003). Individual accessibility revisited: Implications for geographical analysis in the twenty-first century. Geographical Analysis, 35(4), 341–353.
Law, R. (1999). Beyond‘women and transport’: Towards new geographies of gender and daily mobility. Progress in Human Geography, 23(4), 567.
Lei, T., Chen, Y., & Goulias, K. (2012). Opportunity-based dynamic transit accessibility in southern California. Transportation Research Record: Journal of the Transportation Research Board, 2276(1), 26–37.
Litman, T. (2006). Lessons from Katrina and Rita: What major disasters can teach transportation planners. Journal of Transportation Engineering, 132(1), 11–18.
Mamun, S. A., Lownes, N. E. Osleeb, J. P. A method to define public transit opportunity space. Journal of Transport Geography, 28, 144–154. Mavoa, S., Witten, K. McCreanor, T. GIS based destination accessibility via public transit and walking in Auckland, New Zealand. Journal of
Transport Geography, Special Section on Child & Youth Mobility, 20(1), 15–22.
McMenamin, T. (2007). A time to work: Recent trends in shift work andflexible schedules. Monthly Labor Review Available from. Washington, DC: Bureau of Labor Statistics. Accessed 13.11.13.
Miller, H. J. (1999). Measuring space–time accessibility benefits within transportation networks: Basic theory and computational procedures. Geographical Analysis, 31(2), 187–212.
Morang, M., & Pan, L. (2013). GTFS_NATools (0.5.5). Redlands, CA, Available from:〈http://www.transit.melindamorang.com/〉.
Neutens, T., Delafontaine, M. Scott, D. M. An analysis of day-to-day variations in individual space–time accessibility. Journal of Transport Geography, 23, 81–91.
Owen, A. (2013). Modeling the commute mode share of transit using continuous accessibility to jobs. Available from:〈http://conservancy.umn.
edu/handle/11299/162380〉Accessed 12.0514.
Peng R. D. (2012) mvtsplot: Multivariate time series plot. Available from:〈http://cran.r-project.org/web/packages/mvtsplot/index.html〉Accessed 24.11.13.
Polzin, S., Pendyala, R., & Navari, S. (2002). Development of time-of-day-based transit accessibility analysis tool Available from. World Transit Research
Santos, A., McGuckin, N. Nakamoto, H. Y. Summary of travel trends: 2009 national household travel survey. Washington, DC: Federal Highway Administration.
Tomer, A., Kneebone, E. Puentes, R. Missed opportunity: Transit and jobs in metropolitan america Available from:. Washington, DC: Brookings Institution. Accessed 13.01.12.
Verbesselt, J., Hyndman, R. Zeileis, A. Phenological change detection while accounting for abrupt and gradual trends in satellite image time series. Remote Sensing of Environment, 114(12), 2970–2980.
Weber, J., & Kwan, M.-P. (2002). Bringing time back in: A study on the influence of travel time variations and facility opening hours on individual accessibility. The Professional Geographer, 54(2), 226–240.
Zeileis, A., Kleiber, C. Krämer, W. Testing and dating of structural changes in practice. Computational Statistics & Data Analysis, 44(1–2), 109–123.
